As electronic devices become smaller and operate at higher speeds, energy emitted in the form of heat increases dramatically. A popular practice in the industry is to use thermal grease, or grease-like materials, alone or on a carrier in such devices to transfer the excess heat dissipated across physical interfaces. However, the performance of these materials breaks down, e.g. deteriorates, when large deviations from surface planarity cause gaps to form between the mating surfaces in the semiconductor device or when large gaps between mating surfaces are present for other reasons, such as variation in package heights, manufacturing tolerances, etc. When the heat transfer ability of these materials breaks down, the performance of the device is adversely affected. The present invention provides semiconductor assemblies with fibrous interfaces that deal effectively with excess heat that may be dissipated in electronic devices.